Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Abstract

a b s t r a c tWe construct a sheaf of N = 2 vertex algebras naturally associated to any Poisson manifold.The relation of this sheaf to the chiral de Rham complex is discussed. We reprove the result about the existence of two commuting N = 2 superconformal structures on the space of sections of the chiral de Rham complex of a Calabi-Yau manifold, but now calculated in a manifest N = 2 formalism. We discuss how the semi-classical limit of this sheaf of N = 2 vertex algebras is related to the classical supersymmetric non-linear sigma model.